Modelling with functions.

Technology Active – the use of calculator is advised for this assignment.

A new dry-cleaning machine has been designed. At the end of each cleaning cycle, the dry-cleaning liquid will be reduced by evaporation and condensation. Each time the machine is used there is a loss of 2% of the dry-cleaning liquid.

Initially the machine is filled with 1000 mL of dry-cleaning liquid.

How much liquid will remain after the machine has been used once, twice and five times? Give your answers correct to the nearest mL.

Develop a formula that uses indices to determine the amount of liquid A (in mL) left after n uses.

Use your formula to check your answers from question 1.

Sketch the graph of A versus n for . Use appropriate scale on each axis.

Determine which is dependent and which is independent variable.

What name do we give to the graph of A versus n?

Show that after 20 uses the quantity of liquid remaining is approximately two-thirds of the original quantity.

How much liquid will remain after 40 uses? What proportion is this of the original quantity?

If the original quantity of liquid was 2000 mL, change your formula appropriately and redo the calculations for question 8.

Make a comparison of your answers to questions 8 and 9. What do you notice?

When the quantity of liquid is reduced to of the original amount it is time to replace the liquid. After how many uses will the liquid need to be replaced?

What amount of liquid would initially be required if the amount remaining when the liquid needs replacing is 200 ml?